This is an example of a Cubic Function. A cubic function is in the form f(x) = ax3 + bx2 + cx + d. The most basic cubic function is f(x)=x^3 which is shown to the left. The function of the coefficient a in the general equation determines how wide or skinny the function is. The constant d in the equation is the y-intercept of the graph. Another form of cubic functions is f(x) = a(x – h) 3 + k, where a, h, and k are constants and a is not equal to 0. The values of h and k are the horizontal and vertical translation, or shift, of the curve.The graph shifts h units right when h is positive and shifts h units left when h is negative. The graph shifts upwards k units when k is positive and shifts k units downward when k is negative. The graph is flipped upside down (reflected over the x-axis) when -f(x) is negative. The graph is reflected about the y-axis when f(-x). The basic shape of a cubic function has a shape of an "s".
Cubic equations were known to the ancient Babylonians, Greeks, Chinese, Indians, and Egyptians. Methods for solving cubic equations appear in The Nine Chapters on the Mathematical Art, a Chinese Mathematical text compiled around the 2nd century BC by Liu Hui in the 3rd century. In the 7th century, an astronomer mathematician Wang Xiaotong in his treatise titled Jigu Suanjing systematically established and solved 25 cubic equations of the form x^3+px^2+qx=N.
Cubic equations were known to the ancient Babylonians, Greeks, Chinese, Indians, and Egyptians. Methods for solving cubic equations appear in The Nine Chapters on the Mathematical Art, a Chinese Mathematical text compiled around the 2nd century BC by Liu Hui in the 3rd century. In the 7th century, an astronomer mathematician Wang Xiaotong in his treatise titled Jigu Suanjing systematically established and solved 25 cubic equations of the form x^3+px^2+qx=N.
Cubic Function Examples.docx | |
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Real Life Cubic Functions.docx | |
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